Following are digitized figures from the text for use in compounding

Finite height

$\beta$ for finite height effects can be found using the following plot. Note that the finite height plot also includes effects of finite width for a centered crack. If your crack is not centered, you will need to subtract this effect.

In [2]:
import pandas as pd
import numpy as np
import plotly.express as px
import pickle
from IPython.core.display import display, HTML
import plotly.io as pio
pio.renderers.default = "notebook"

#this is to show images from text
from IPython.display import Image
Image(filename='height.jpg',width=200)
Out[2]:
In [3]:
#load saved plot.ly figures
with open('../plotlyfigs/compounding.pickle','rb') as f:
    fig=pickle.load(f)

#function to plot figure and make csv file
def plotFig(f,mytitle):
    arrays = []
    data = []
    x = f['layout']['xaxis']['title']
    xtitle = x
    y = f['layout']['yaxis']['title']
    if y == 'beta':
        ytitle = r'$\beta$'
    else:
        ytitle = y
    title = f['layout']['title']
    for i in range(len(f['data'])):
        arrays.extend([f['data'][i]['name']]*2)
        data.append(f['data'][i]['x'])
        data.append(f['data'][i]['y'])
    arrays = [arrays,[x,y]*len(f['data'])]
    tuples = list(zip(*arrays))
    data_t = [list(j) for j in zip(*data)]
    index = pd.MultiIndex.from_tuples(tuples, names=['name', 'axis'])
    df = pd.DataFrame(data_t, columns=index)
    #export data to csv
    df.to_csv(mytitle)
    #plot data
    myfig = px.line(df.stack(0).reset_index(), x=x, y=y, color="name", title=title, labels={x:xtitle, y:ytitle, 'name':'height ratio'})
    myfig.show()
    display(HTML("<a href=\""+mytitle+"\">Download .csv</a>"))
    
#plot finite height figure
plotFig(fig[0],'finiteheight.csv')
Download .csv

Offset internal crack

$\beta$ for offset internal cracks can be found using the following plot. Note that there are two $\beta$ values, one near the edge, (Tip A), and the other away from the edge (Tip B).

You may have to refer to this chart twice to consider the effects of two edges.

In [4]:
Image(filename='edge.jpg',width=200)
Out[4]:
In [5]:
plotFig(fig[1],'offsetedge.csv')
Download .csv

Cracks near a hole

For cracks near a hole, the following two charts can be used to find $\beta$. Note that you will find one $\beta$ per hole per crack tip. Tip A refers to the tip farthest from the hole, Tip B is the tip closest to the hole

In [6]:
Image(filename='hole.jpg',width=400)
Out[6]:
In [7]:
plotFig(fig[2],'nearholeA.csv')
Download .csv
In [8]:
plotFig(fig[3],'nearholeB.csv')
Download .csv
In [ ]: